Let the man's age be ab and the son's age be ba.
Now we are given that the sum of their ages is 66.
So ab + ba = 66
=> 10a + b + 10b + a = 66
=> 11a + 11b = 66
=> a + b = 6
If a = 6 , b = 0
If a = 5, b = 1
If a = 4, b = 2
For values of a = 3 , 2 , 1 and 0 the son's age is no longer less than the man.
Therefore the age of the man and the son can be
(60, 6), (51 ,15) and (42 , 24)
Let the age of the father is presented by the 2 digit number xy.
Then, the son's age is the 2 digit number yx.
==> The fathers age = 10x + y
==. The son's age = 10y + x
But we know that the sum of their ages is 66.
==> 10x + y + 10y + x = 66
==> 11x + 11y = 66
We will divide by 11
==> x + y = 6
Then the sum of the digit must be 6.
Let us determine the positive integers whose sums are 6.
==> 0 + 6 = 6
Then the fathers age = 60
and the son's age = 06
Also, : 2 + 4 = 6
==> The father's age = 42
The son's age = 24
Also, 5 + 1 = 6
==> The fathers age = 51
The son's age = 15
Also, 3 + 3 = 6
==> The father's age = 33
The son's age = 33
But this solution is impossible because the father's and son's age can not be the same.
Then, possible answers are:
( 51 and 15 ) (24 and 42) and ( 60 and 6)